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Journal of Lie Theory 14 (2004), No. 1, 215--226
Copyright Heldermann Verlag 2004
Asymptotic Products and Enlargibility of Banach-Lie Algebras
D. Beltita
Romanian Academy of Sciences,
Institute of Mathematics "Simion Stoilow",
P.O. Box 1-764,
70700 Bucharest,
Romania,
dbeltita@imar.ro
The paper provides a "standard" proof of a local theorem on the enlargibility
of Banach-Lie algebras. A particularly important special case of that theorem
is that a Banach-Lie algebra is enlargible provided it has a dense locally
finite subalgebra. The theorem is due to V. Pestov, who proved it by techniques
of nonstandard analysis. The present proof uses a theorem concerning the
enlargibility of asymptotic products of contractive Banach-Lie algebras.
Keywords: asymptotic product, enlargible Banach-Lie algebra.
MSC 2000: 22E65, 17B65, 46B08.
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